cp's OEIS Frontend

A341134 Number of ways to write n as an ordered sum of 5 prime powers (including 1).

%I A341134 #6 Feb 05 2021 18:43:12
%S A341134 1,5,15,35,70,121,190,280,395,535,711,920,1160,1425,1725,2041,2395,
%T A341134 2775,3200,3645,4146,4640,5190,5730,6325,6915,7625,8270,9030,9745,
%U A341134 10576,11320,12320,13185,14305,15281,16510,17480,18855,19835,21306,22435,24010,25025,26810,27790,29590
%N A341134 Number of ways to write n as an ordered sum of 5 prime powers (including 1).
%p A341134 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341134 b:= proc(n, t) option remember;
%p A341134       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341134       `if`(q(j), b(n-j, t-1), 0), j=1..n)))
%p A341134     end:
%p A341134 a:= n-> b(n, 5):
%p A341134 seq(a(n), n=5..51);  # _Alois P. Heinz_, Feb 05 2021
%t A341134 nmax = 51; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341134 Cf. A000961, A010055, A282062, A282064, A341123, A341133, A341135, A341136, A341137, A341138, A341139.
%K A341134 nonn
%O A341134 5,2
%A A341134 _Ilya Gutkovskiy_, Feb 05 2021